When Em Johnson received a letter offering her a place on an MA course in social work at London Metropolitan university, she was thrilled. Caring for others was what she wanted to do. Sitting down at the kitchen table examining the costs of studying, however, it dawned on her: this vital step towards the job she yearned to do was impossible. The numbers did not add up. "It was the rent. I simply could not afford to live."

Today, seven years later, Johnson, 28, who lives in Hanwell, west London, with her husband and two-year-old son, is a substance misuse worker at a GP's surgery. She still yearns to join her chosen profession, but it still isn't possible. "The social work course is essentially a nine-to-five job with no payment, plus all the academic side. I had worked throughout my undergraduate degree to get by, but even that was not possible if I wanted to do this postgraduate course," she said.

"We have done everything in the right order: a mortgage at 22, married at 23, we don't live an extravagant lifestyle – but I just can't make this next step to do the job I want."

Johnson's story is typical of thousands who, on completion of their undergraduate degrees, need to develop their skills to take the next step, be it in a profession or academia, but cannot because they are not from wealthy families, do not have easy access to credit or cannot find a sponsor.

The problem itself is not new. But what is troubling many is its growing scale and seriousness, prompting vice chancellors from leading universities across the UK to talk of a looming "catastrophe" both for social mobility and the British economy.

When the undergraduate system was reformed, in line with the recommendations of former BP chief executive Lord Browne, to allow universities to charge up to £9,000 a year for courses, postgraduate course fees quietly followed to make up for the huge cut in finance from central government for teaching. The latest figures show an 11% fee increase this year – and the universities predict that will be just the start.

Facing huge financial pressures, research councils – the public bodies that award grants for academic research – have completely withdrawn support for people taking standalone taught master's degrees (usually one-year courses that do not form part of a PhD).

Meanwhile, last year banks agreed to give professional and career development loans to fewer than half (44%) of the 22,716 people who applied, and then only at onerous interest rates.

Inevitably, the latest figures show that there were over 8,000 fewer UK students taking up taught postgraduate courses in 2010-11 than the year before, a 4.3% contraction. This year's figures, due out on Thursday, are expected to be worse still.

But it is in a year and a half that the true postgraduate crisis looms, senior academics say. Then it will be the turn of the students loaded with debts from the new system to decide whether they can afford to do more studying.

Students from wealthy backgrounds may be able to afford to study the subjects they need to grab the best jobs and the biggest salaries. Foreign students, particularly from China and Brazil, are flocking to the UK for postgraduate courses – often supported by their governments, who spy a chance to grab a top-class education without establishing their own expensive institutions. But for the majority of home UK students, this world-class education may be out of reach.

Now, 11 leaders of universities in England, Scotland, Wales and Northern Ireland have condemned the existence of a "policy vacuum" where there should be a funding model for would-be postgraduate students, as Professor Simon Gaskell, the vice chancellor of Queen Mary, University of London, puts it.

The absence of such a scheme for "an advanced economy that needs high level technical skills and workforce flexibility" is a "catastrophe", according to Professor Don Nutbeam of Southampton University, or, in the words of Professor Jules Pretty, deputy vice-chancellor at Essex university, a "ticking timebomb".

The situation is less serious in Northern Ireland and Scotland than England and Wales. In Scotland, the number of UK students undertaking taught postgraduate courses at Edinburgh University is not growing as well as the vice chancellor, Sir Tim O'Shea, would like, but students will not face the same debt as those south of the border because fees have not trebled. In Northern Ireland, the executive has pumped money into universities as an economic stimulus and the institutions are using the cash to fund research degrees. But the vice chancellor at Queen's University, Belfast, Professor Sir Peter Gregson, says the lack of a funding model for students who need to do a taught master's course also worries him.

The problem demands action, according to Professor Thomas Docherty of Warwick University, who sits on the steering committee of a newly formed campaign group, the Council for the Defence of British Universities. "There is a massive problem already emerging here and we are very concerned by it," he said. "Postgraduate funding has been totally neglected. It is almost as if the government thinks the problem will go away, will sort itself out."

The council, whose members include Lord Bragg, Sir David Attenborough and Professor Richard Dawkins, believes it is one of the biggest issues facing the country and is meeting this month to find a solution. But the academics who are now voicing their fears – from Edinburgh to Exeter and Belfast to East London – know that it will be the government that needs to take the bull by the horns. "We have got a year and a half to get this right before this cohort, who are paying £9,000 in undergraduate fees, come through to make a decision on postgraduate study," Pretty said. "We need some sort of loan system by then, otherwise the home market is likely to evaporate."

"We are getting very nervous as it gets closer and closer," admitted Professor Trevor McMillan, pro-vice-chancellor for research at Lancaster university. Professor Robert Allison, vice-chancellor at Loughborough university, added: "People are sort of ducking the issue. We need someone to say that we are going to solve this."